4. Foreign Exchange Intervention and the Exchange Rate In Zambia
3.3 Unit Root Tests
Variable levels 1st difference Integration order
m2 -2.92 -12.97** I(1)
m1 -1.58 -10.96* I(1)
p 2.267 -6.45** I(1)
y -4.223** I(0)
idep -0.45 -6.667** I(1)
itbill -2.69 -5.193** I(1)
ibond -4.355** I(0)
deficit -1.799 -12.67** I(1)
P*ssa -1.43 -7.76** I(1)
P*usa -3.23 9.082** I(1)
erand -1.593 -7.73** I(1)
edollar -3.23 -8.01** I(1)
debt -1.239 -8.962** I(1)
*(**) significant at (5%),(1%) levels of significance Tests were obtained using the Phillips Perron method
and its first difference (monthly inflation) in the upper panel of figure 2. For most of the sample period, inflation has been fairly stable. Large fluctuations are observed in the early part of the sample, which are the early years after the reforms, and periods of very high inflation.
M1 and M2 are used in the estimation alternately. In Figure 3.3 we plot the log levels in the upper panel, monthly growth in the middle panel and the real series ( deflated by the CPI) in the lower panel. The real series are mean adjusted. The Phillips-Peron tests show that the series exhibit a unit root in nominal terms. The series are however stationary in first differences.
We use three interest rates in the study and these are plotted in figure 3.4 The three-month treasury bill rate is used as the alternate interest rate, the average deposit rate as the own interest rate and the 12-month bond rate as the long rate. The 12-month bond was the longest period bond available for most of the sample period. The three interest rates are quite highly correlated
1995 2000 4.5
5.0 5.5 6.0 6.5
log of the Consumer Price Index
1995 2000
0.000 0.025 0.050
0.075 CPI monthly Inflation
0 20 40 60 80 100
5.50 5.75 6.00
6.25 log of Output
0 20 40 60 80 100
−1.0
−0.5 0.0
0.5 growth in output
Fig. 3.2: Prices and Output
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
12 13 14
15 log of M1 log of M2
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
−0.1 0.0 0.1
0.2 growth rate of M1 growth rate of M2
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
7.00 7.25
7.50 log of real M1 log of real M2
Fig. 3.3: Monetary Aggregates
early in the sample until mid-1996 when the bond rate sharply declines for a few months and begins to increase again. The deposit rate begins to decline in late 1997 and the spread from the treasury bill rate continues to widen for the rest of the sample period. The unit root tests show that the deposit and bond rates are stationary although there is a possible structural break in early 1998.
We redo the test starting December 1994 and the deposit rate is now I(1). The statistic reported in the table reflects the later.
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
20 40 60 80 100 120
3−month Treasury bill rate average deposit rate
12−month bond rate
Fig. 3.4: Interest Rates
The nominal exchange rate is measured by the rate of the kwacha to the rand and the kwacha to the dollar. These rates are used alternately in the
estimations. For the foreign prices, we use the South African CPI (p∗ssa) and the US wholesale price index (p∗usa). The South African variables were chosen because South Africa is Zambia’s major trading partner especially in consumer goods and it was thought an appropriate alternative to averaging over major trading partners . The use of the US variables is motivated by the fact that most official transactions are conducted using the US dollar. We plot these variables in figure 3.5 below. We also plot in the bottom panel the real
exchange rates for both the dollar and the rand defined as the log of the domestic price minus the log of the foreign price and log of the relevant exchange rate. The exchange rate has been increasing over time although a short period of decline is observed shortly before the 2001 elections. The prices and nominal exchange rates have a unit root and stationary in first differences. The dollar real rate is stationary while that of the rand is not.
1995 2000
4.60 4.65 4.70
4.75 log of US wholesale Price log of South African CPI
1995 2000
−0.01 0.00 0.01
0.02 South African Monthly inflation US monthly wholesale inflation
1995 2000
7 8
Kwacha to dollar exchnage rate kwacha to rand exchange rate
1995 2000
−0.1 0.0 0.1
0.2 kwacha to dollar depreciation rate kwacha to rand depreciation rate
1995 2000
−6.5
−6.0 real kwacha to dollar exchange rate real kwacha to rand exchange rate
Fig. 3.5: Foreign Prices and Exchange Rates
We also use domestic debt as measured by government securities outstanding (treasury bills plus government bonds)as a fiscal measure. The series and its growth rates are plotted in figure 3.6 below. The variables in levels move together until 1998 when domestic debt shows a downward trend but begins to rise again after 2000. The growth series exhibit a lot of volatility for both variables.
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 12.0
12.5 13.0 13.5 14.0
log of domestic debt
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
−0.1 0.0 0.1
0.2 growth rate of domestic debt
Fig. 3.6: Domestic Debt
3.6 Estimation Results
We begin our discussion of the results with the forecasting experiments and then move on to discuss the estimation of the inflation equation. All estimations that involve the interest rates are done from December 1994 to avoid the possible structural break. We include seasonal dummies in both the forecasting and single equation estimations. In the forecasting experiments, we explore the information content of the financial variables by looking at the relationships between prices and different possible information variables.
These forecasting experiments are done in an auto regression setting as shown in equation ( 3.3). In the inflation equation, our interest is to see if the financial variables and in particular the monetary aggregates enter the
inflation equation significantly. This is particularly important in that it allows us to check the performance of the variables when we control for the presence of other variables. It has often been argued that when interest rates are added, money tends to loose its explanatory power.
3.6.1 Forecasting
In this section, we discuss the forecasting experiments. The forecasts are all out of sample forecasts.The focus on out of sample forecasting experiments is an attempt to simulate real time policy decision making. Since the data used are revised, the type of information available to us differs from that available to the decision maker at the central bank. Each model is composed of the price level and one possible information variable. Each forecast is a one step ahead forecast over a moving window of four years. One step ahead forecasts were preferred as a way of mimicking the horizon the central bank faces given the data. The initial estimation is done between January 1994 and December 1997. We then make a forecast for January 1998. Then the estimation sample is rolled over to start February 1994 and end January 1998 and then we make a forecast for February 1998 and so on.
We then calculate the MAPE based on ( 3.7) to decide if a variable adds significant information for forecasting or not. This decision is based on the relative performance of a benchmark model. The benchmark model used is the best fitted autoregressive model for the price level. Preliminary analysis showed that the best fit model was an AR(1) model and this can be seen from Figure 3.10 in the appendix which shows the correlation function for the price level . We therefore estimate an AR(1) model as the base model. This model is also estimated using rolling regressions over the same moving window. The higher the MAPE for a model relative to the benchmark model, the less information the additional variable has for forecasting inflation. This approach is superior to just looking at the performance of one model for our interest because it allows us to compare ’competing’ information variables. More importantly, we can check the importance of the information from the
monetary aggregates relative to information from other variables by comparing their MAPEs.
The data are used in log levels. The use of rolling regression precludes the use of co-integration in this analysis as co-integration was only identified at a few